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Mean vs. Median Life Expectancy for Retirement Planning

A reader writes in, asking:

“Your discussion of life expectancies this week got me thinking. I believe that the life expectancy that is often discussed is the ‘mean’ life expectancy. Is that true? And if so, how do the ‘median’ and ‘mode’ life expectancies compare? Is mean life expectancy really the best thing to use for retirement planning?”

Yes, it is true that life expectancy refers to mean (i.e., average) life expectancy unless explicitly stated otherwise. And it is true that, as with many other things, it can be informative to look median and mode life expectancies as well.

However, in short, when it comes to retirement planning (at least for somebody retiring at a typical age) mean life expectancy does in fact do a pretty reasonable job of expressing how long the average person is likely to live.

As a brief refresher for anybody who hasn’t used these terms in a while:

Mean refers to what we normally call “average,”

Median refers to the middle data point in our set, and

Mode refers to the most common value.

So with regard to lifespans:

Mean life expectancy would be the average age at death,

Median life expectancy would be the age which 50% of people will die prior to reaching, and which 50% of people will live past, and

Mode life expectancy would be the most common age at death.

Mean, Median, Mode Life Expectancy at Birth

According to the SSA’s 2014 period life table*, male life expectancy at birth is 76 years. That’s the mean value. The median life expectancy is just past age 80. And the mode (i..e, most common) age at death is age 86.

Why the difference?

It occurs because with a life expectancy of 76 years, there is of course a chance that a person dies far, far before reaching that life expectancy. For instance, infant mortality is tragic but unfortunately not super rare. About 0.6% of babies die before their first birthday. In such a case, a person will have fallen 75 years short of their life expectancy.

There is, on the other hand, basically no chance that a person will live 75 years past their life expectancy (i.e., to age 151). So in order for the mean to be the mean, there must be many more people living past it in order to balance out the smaller number of people who come nowhere near to reaching it.

You can see this phenomenon in the following chart, which shows frequency of male deaths at various ages. There is a narrow but long tail to the lefthand side of the distribution, representing all the people who die long before reaching their life expectancy. There is no such tail on the righthand side.

The blue line in the chart shows mean life expectancy. As you can see, it occurs well before the mode age at death (i.e., the point at which the chart peaks, at age 86).

The same relationship holds true for females at birth, for the same reasons. Specifically, according to the SSA’s 2014 period life table:

Mean life expectancy at birth is 81 years,

Median life expectancy at birth is roughly 84.5 years, and

Mode age at death is 89 years.

Overall point being: a person’s life expectancy at birth somewhat understates how long they are actually likely to live.

Mean, Median, Mode Life Expectancy for Retirement Planning

But when it comes to retirement planning, the differences are much smaller.

For instance, for a 60 year old male:

Mean age at death is 81.5 years,

Median age at death is 82.5 years, and

Mode at age death is 86 years.

And for a 60 year old female:

Mean age at death is 84.5 years,

Median age at death is 86 years, and

Mode age at death is 89 years.

The reason the differences are much smaller here is that, if you’re already age 60, that long lefthand tail on the distribution turned out not to apply to you. The remaining distribution is much more symmetrical. In other words, you’re now about as likely to die before reaching your life expectancy as you are to live past your life expectancy.

Overall point being: for the sake of retirement planning, mean life expectancy does a decent job of representing how long you are likely to live.

*Of note: All of the data in this article comes from the SSA’s 2014 Period Life Table. I’m using it here because it provides the most accessible data to work with, and because it can accurately demonstrate the relationship between mean, median, and mode. However, as we discussed last week, period life tables (and therefore all of the figures used here) somewhat understate a person’s life expectancy.

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